Statement-1: If A is an orthogonal matrix of order n, then $adj (adj\, A) |=±1$

Statement-2: $|adj (adj\, A)| = |A|^{n^2 – 1}$

Statement-1 is True, Statement-2 is False. 

We have known that $|adj (adj\, A)| = |A|^{(n − 1)^2}$.

So, statement-2 is false.

If A is an orthogonal matrix, then $|A|= ±1$

$∴|adj (adj\, A)|=|A|^{(n-1)^2} =(±1)^{(n-1)^2}=±1$